In the context of global warming, efforts have been made for some time to reduce the emission of greenhouse gases, in particular CO2, to the atmosphere. Numerous advances have already been made in this respect, leading to the CO2 generated during the combustion of fossil fuels being partly to completely separated out. In this context, the generation of electrical energy by firing combustion chambers for driving gas turbine plants, the exhaust emissions from which form a not inconsiderable proportion of the volume of emissions discharged to atmosphere by man-made sources, is of particular interest in this context. With a view to reducing the discharge of CO2 to the open atmosphere which is caused by gas turbine plants, there are known techniques for separating CO2 out of the exhaust gas stream from gas turbine plants, which by recirculating the exhaust gas stream separate out CO2 at the highest possible pressure. It is fundamentally the case that the higher the CO2 partial pressure in the exhaust gas stream, the better the efficiency of CO2 separation. To increase the pressure of the exhaust gas stream, the latter is compressed, in a manner known per se, by means of the combustion feed air compressor unit of the gas turbine plant, the recirculated exhaust gas being diluted with fresh air, with the result that, on the one hand the oxygen content of the combustion feed air which is to be compressed by the compressor unit and furthermore also the CO2 concentration of the recirculated exhaust gas are reduced. As a result of the lower oxygen content of the compressed mixed air formed by the recirculated exhaust-gas routing, which, as it flows on through the gas turbine plant, is then fed to the burner, in which the mixed air is converted into an ignitable fuel/air mixture by admixing fuel, and is finally ignited in the combustion chamber, in particular in certain circumstances what is known as combustion instability occurs, in which the combustion within the combustion chamber takes place without any excess oxygen. Combustion instability of this nature on the one hand leads to high CO emissions and on the other hand leads to the formation of thermo-acoustic oscillations, which can greatly impair operation of the gas turbine plant. On the other hand, the CO2 content, which has been reduced by mixing with combustion feed air, in the recirculated, compressed exhaust gas flow leads to a lower efficiency of CO2 separation. The invention is intended to remedy this situation and provide a way of operating gas turbine plants which allows efficient separation of CO2 out of the recirculated exhaust gas flow without having a long-term effect on the stable burner properties.